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The Utility of Sparse Error Detection in Quantum Simulations
Authors:
Henry Froland,
Dorota M. Grabowska,
Sebastian Grieninger,
Jeremy Hartse,
Anne L. Lashbrook,
Zhiyao Li,
Ziyuan Li,
Sarah J. M. Powell,
Martin J. Savage,
Xiaojun Yao,
Nikita A. Zemlevskiy
Abstract:
The recent success of error detecting codes points toward their potential application to fault-tolerant simulations of nature. In this work, we examine the utility of sparse error detection for simulating lattice gauge theories using quantum computers. In particular, we study the time evolution of the lattice Schwinger model embedded into the Iceberg code family, $[[N+2, N, 2]]$, as well as the Hy…
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The recent success of error detecting codes points toward their potential application to fault-tolerant simulations of nature. In this work, we examine the utility of sparse error detection for simulating lattice gauge theories using quantum computers. In particular, we study the time evolution of the lattice Schwinger model embedded into the Iceberg code family, $[[N+2, N, 2]]$, as well as the Hypercube code family, $[[2^N, N, 2]]$. The lattice of electrons and positrons in the axial gauge is embedded into a single code block or into multiple code blocks, and this work finds that large codeblocks are advantageous in the absence of connectivity constraints. Noisy classical simulations with realistic near-term error rates, infrequent syndrome measurements and physics-aware postselection are found to improve observable estimation. Under realistic noise rates for near-term quantum computers, this work finds that sparse error detection in quantum simulations has the potential to improve accuracy of observable estimation. Additional rounds of error detection are found to systematically drive errors in observables to the noise floor set by the code. These findings suggest that incorporating minimal implementations of fault tolerance in the near-term will enhance the performance of quantum simulations in nuclear physics and high-energy physics.
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Submitted 3 August, 2026;
originally announced August 2026.
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Realizing Error Suppression in Partially Fault-Tolerant Quantum Simulations with IBM Quantum Computers
Authors:
Henry Froland,
Dorota M. Grabowska,
Sebastian Grieninger,
Jeremy Hartse,
Anne L. Lashbrook,
Zhiyao Li,
Ziyuan Li,
Sarah J. M. Powell,
Martin J. Savage,
Xiaojun Yao,
Nikita A. Zemlevskiy
Abstract:
Quantum error-detecting codes offer a near-term path for improving the performance of quantum simulations on noisy hardware. Using IBM's superconducting quantum computer ibm_boston, we show that partially fault-tolerant encoded quantum simulations of the Ising model in 1+1D and 2+1D outperform their unencoded counterparts in estimating local observables. To represent 42 logical qubits on the heavy…
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Quantum error-detecting codes offer a near-term path for improving the performance of quantum simulations on noisy hardware. Using IBM's superconducting quantum computer ibm_boston, we show that partially fault-tolerant encoded quantum simulations of the Ising model in 1+1D and 2+1D outperform their unencoded counterparts in estimating local observables. To represent 42 logical qubits on the heavy-hex quantum processor, 21 blocks of the [[4, 2, 2]] Iceberg code and up to 136 physical qubits are used. By pairing fault-tolerant syndrome extraction with non-fault-tolerant logical operations, this scheme preserves many of the benefits of error detection while avoiding the overhead typically required for a fully fault-tolerant logical gate set. The encoding's square logical connectivity, together with the freedom to place logical qubits within each block, enables simulations of a 2D spatial lattice with lower circuit depth than the unencoded implementation requires. We introduce Observable-Ranked Postselection, a selective-filtering technique based on syndrome correlations that recovers reliable results without the prohibitive shot loss of full syndrome postselection. Under the cumulative effect of device errors, this encoding improves local-observable accuracy over the unencoded baseline by 2-6% at intermediate times in 1+1D simulations, growing with circuit depth to over 200% in 2+1D at the latest times studied.
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Submitted 27 July, 2026;
originally announced July 2026.
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Measuring Non-Stabilizerness in an SU(2) Lattice Gauge Theory
Authors:
Henry Froland,
Dorota M. Grabowska
Abstract:
One of the goals of quantum simulation is to provide novel insights into quantum systems, such as the gauge theories that are relevant for high-energy and nuclear physics. Recent years have seen rapid improvements in both the hardware and software necessary for these simulations. A central consideration in the design of such simulations is the quantum complexity of a given quantum state. This work…
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One of the goals of quantum simulation is to provide novel insights into quantum systems, such as the gauge theories that are relevant for high-energy and nuclear physics. Recent years have seen rapid improvements in both the hardware and software necessary for these simulations. A central consideration in the design of such simulations is the quantum complexity of a given quantum state. This work takes a step towards studying a specific kind of complexity, namely the non-stabilizerness, in a simple yet non-trivial system: SU(2) lattice gauge theory of two plaquettes. The non-stabilizerness of low-energy eigenstates is studied and the implications for quantum simulations are discussed. The real-time evolution of this system is simulated on ibm_marrakesh and the non-stabilizerness is measured using a random measurement protocol. New techniques enhancing the efficiency of this protocol are developed, including both a new way to calculate the estimator for non-stabilizerness and a flexible error mitigation technique called Bit String Decoherence Renormalization. This mitigation method is central to accurately resolving the experimental time dependence of non-stabilizerness, and is anticipated to have broad applicability in digital quantum simulations.
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Submitted 12 June, 2026;
originally announced June 2026.
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Simulating Fully Gauge-Fixed SU(2) Hamiltonian Dynamics on Digital Quantum Computers
Authors:
Henry Froland,
Dorota M. Grabowska,
Zhiyao Li
Abstract:
Quantum simulations of many-body systems offer novel methods for probing the dynamics of the Standard Model and its constituent gauge theories. Extracting low-energy predictions from such simulations rely on formulating systematically-improvable representations of lattice gauge theory Hamiltonians that are efficient at all values of the gauge coupling. One such candidate representation for SU(2) i…
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Quantum simulations of many-body systems offer novel methods for probing the dynamics of the Standard Model and its constituent gauge theories. Extracting low-energy predictions from such simulations rely on formulating systematically-improvable representations of lattice gauge theory Hamiltonians that are efficient at all values of the gauge coupling. One such candidate representation for SU(2) is the fully gauge-fixed Hamiltonian defined in the mixed basis. This work focuses on the quantum simulation of the smallest non-trivial system: two plaquettes with open boundary conditions. A mapping of the continuous gauge field degrees of freedom to qubit-based representations is developed. It is found that as few as three qubits per plaquette is sufficient to reach per-mille level precision on predictions for observables. Two distinct algorithms for implementing time evolution in the mixed basis are developed and analyzed in terms of quantum resource estimates. One algorithm has favorable scaling in circuit depth for large numbers of qubits, while the other is more practical when qubit count is limited. The latter algorithm is used in the measurement of a real-time observable on IBM's Heron superconducting quantum processor, ibm_fez. The quantum results match classical predictions at the percent-level. This work lays out a path forward for two- and three-dimensional simulations of larger systems, as well as demonstrating the viability of mixed-basis formulations for studying the properties of SU(2) gauge theories at all values of the gauge coupling.
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Submitted 27 December, 2025;
originally announced December 2025.
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A Fully Gauge-Fixed SU(2) Hamiltonian for Quantum Simulations
Authors:
Dorota M. Grabowska,
Christopher F. Kane,
Christian W. Bauer
Abstract:
We demonstrate how to construct a fully gauge-fixed lattice Hamiltonian for a pure SU(2) gauge theory. Our work extends upon previous work, where a formulation of an SU(2) lattice gauge theory was developed that is efficient to simulate at all values of the gauge coupling. That formulation utilized maximal-tree gauge, where all local gauge symmetries are fixed and a residual global gauge symmetry…
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We demonstrate how to construct a fully gauge-fixed lattice Hamiltonian for a pure SU(2) gauge theory. Our work extends upon previous work, where a formulation of an SU(2) lattice gauge theory was developed that is efficient to simulate at all values of the gauge coupling. That formulation utilized maximal-tree gauge, where all local gauge symmetries are fixed and a residual global gauge symmetry remains. By using the geometric picture of an SU(2) lattice gauge theory as a system of rotating rods, we demonstrate how to fix the remaining global gauge symmetry. In particular, the quantum numbers associated with total charge can be isolated by rotating between the lab and body frames using the three Euler angles. The Hilbert space in this new `sequestered' basis partitions cleanly into sectors with differing total angular momentum, which makes gauge-fixing to a particular total charge sector trivial, particularly for the charge-zero sector. In addition to this sequestered basis inheriting the property of being efficient at all values of the coupling, we show that, despite the global nature of the final gauge-fixing procedure, this Hamiltonian can be simulated using quantum resources scaling only polynomially with the lattice volume.
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Submitted 16 September, 2024;
originally announced September 2024.
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Sequency Hierarchy Truncation (SeqHT) for Adiabatic State Preparation and Time Evolution in Quantum Simulations
Authors:
Zhiyao Li,
Dorota M. Grabowska,
Martin J. Savage
Abstract:
We introduce the Sequency Hierarchy Truncation (SeqHT) scheme for reducing the resources required for state preparation and time evolution in quantum simulations, based upon a truncation in sequency. For the $λφ^4$ interaction in scalar field theory, or any interaction with a polynomial expansion, upper bounds on the contributions of operators of a given sequency are derived. For the systems we ha…
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We introduce the Sequency Hierarchy Truncation (SeqHT) scheme for reducing the resources required for state preparation and time evolution in quantum simulations, based upon a truncation in sequency. For the $λφ^4$ interaction in scalar field theory, or any interaction with a polynomial expansion, upper bounds on the contributions of operators of a given sequency are derived. For the systems we have examined, observables computed in sequency-truncated wavefunctions, including quantum correlations as measured by magic, are found to step-wise converge to their exact values with increasing cutoff sequency. The utility of SeqHT is demonstrated in the adiabatic state preparation of the $λφ^4$ anharmonic oscillator ground state using IBM's quantum computer ${\textit ibm\_sherbrooke}$. Using SeqHT, the depth of the required quantum circuits is reduced by $\sim 30\%$, leading to significantly improved determinations of observables in the quantum simulations. More generally, SeqHT is expected to lead to a reduction in required resources for quantum simulations of systems with a hierarchy of length scales.
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Submitted 19 September, 2025; v1 submitted 18 July, 2024;
originally announced July 2024.
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A new basis for Hamiltonian SU(2) simulations
Authors:
Christian W. Bauer,
Irian D'Andrea,
Marat Freytsis,
Dorota M. Grabowska
Abstract:
Due to rapidly improving quantum computing hardware, Hamiltonian simulations of relativistic lattice field theories have seen a resurgence of attention. This computational tool requires turning the formally infinite-dimensional Hilbert space of the full theory into a finite-dimensional one. For gauge theories, a widely-used basis for the Hilbert space relies on the representations induced by the u…
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Due to rapidly improving quantum computing hardware, Hamiltonian simulations of relativistic lattice field theories have seen a resurgence of attention. This computational tool requires turning the formally infinite-dimensional Hilbert space of the full theory into a finite-dimensional one. For gauge theories, a widely-used basis for the Hilbert space relies on the representations induced by the underlying gauge group, with a truncation that keeps only a set of the lowest dimensional representations. This works well at large bare gauge coupling, but becomes less efficient at small coupling, which is required for the continuum limit of the lattice theory. In this work, we develop a new basis suitable for the simulation of an SU(2) lattice gauge theory in the maximal tree gauge. In particular, we show how to perform a Hamiltonian truncation so that the eigenvalues of both the magnetic and electric gauge-fixed Hamiltonian are mostly preserved, which allows for this basis to be used at all values of the coupling. Little prior knowledge is assumed, so this may also be used as an introduction to the subject of Hamiltonian formulations of lattice gauge theories.
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Submitted 21 July, 2023;
originally announced July 2023.
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Gravitational Wave Backgrounds from Colliding ECOs
Authors:
Hannah Banks,
Dorota M. Grabowska,
Matthew McCullough
Abstract:
Long baseline atom interferometers offer an exciting opportunity to explore mid-frequency gravitational waves. In this work we survey the landscape of possible contributions to the total 'gravitational wave background' in this frequency band and advocate for targeting this observable. Such an approach is complimentary to searches for resolved mergers from individual sources and may have much to re…
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Long baseline atom interferometers offer an exciting opportunity to explore mid-frequency gravitational waves. In this work we survey the landscape of possible contributions to the total 'gravitational wave background' in this frequency band and advocate for targeting this observable. Such an approach is complimentary to searches for resolved mergers from individual sources and may have much to reveal about the Universe. We find that the inspiral phases of stellar-mass compact binaries cumulatively produce a signal well within reach of the proposed AION-km and AEDGE experiments. Hypothetical populations of dark sector exotic compact objects, harbouring just a tiny fraction of the dark energy density, could also generate signatures unique to mid- and low-frequency gravitational wave detectors, providing a novel means to probe complexity in the dark sector.
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Submitted 15 February, 2023;
originally announced February 2023.
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Overcoming exponential volume scaling in quantum simulations of lattice gauge theories
Authors:
Christopher F. Kane,
Dorota M. Grabowska,
Benjamin Nachman,
Christian W. Bauer
Abstract:
Real-time evolution of quantum field theories using classical computers requires resources that scale exponentially with the number of lattice sites. Because of a fundamentally different computational strategy, quantum computers can in principle be used to perform detailed studies of these dynamics from first principles. Before performing such calculations, it is important to ensure that the quant…
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Real-time evolution of quantum field theories using classical computers requires resources that scale exponentially with the number of lattice sites. Because of a fundamentally different computational strategy, quantum computers can in principle be used to perform detailed studies of these dynamics from first principles. Before performing such calculations, it is important to ensure that the quantum algorithms used do not have a cost that scales exponentially with the volume. In these proceedings, we present an interesting test case: a formulation of a compact U(1) gauge theory in 2+1 dimensions free of gauge redundancies. A naive implementation onto a quantum circuit has a gate count that scales exponentially with the volume. We discuss how to break this exponential scaling by performing an operator redefinition that reduces the non-locality of the Hamiltonian. While we study only one theory as a test case, it is possible that the exponential gate scaling will persist for formulations of other gauge theories, including non-Abelian theories in higher dimensions.
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Submitted 8 December, 2022;
originally announced December 2022.
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Efficient quantum implementation of 2+1 U(1) lattice gauge theories with Gauss law constraints
Authors:
Christopher Kane,
Dorota M. Grabowska,
Benjamin Nachman,
Christian W. Bauer
Abstract:
The study of real-time evolution of lattice quantum field theories using classical computers is known to scale exponentially with the number of lattice sites. Due to a fundamentally different computational strategy, quantum computers hold the promise of allowing for detailed studies of these dynamics from first principles. However, much like with classical computations, it is important that quantu…
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The study of real-time evolution of lattice quantum field theories using classical computers is known to scale exponentially with the number of lattice sites. Due to a fundamentally different computational strategy, quantum computers hold the promise of allowing for detailed studies of these dynamics from first principles. However, much like with classical computations, it is important that quantum algorithms do not have a cost that scales exponentially with the volume. Recently, it was shown how to break the exponential scaling of a naive implementation of a U(1) gauge theory in two spatial dimensions through an operator redefinition. In this work, we describe modifications to how operators must be sampled in the new operator basis to keep digitization errors small. We compare the precision of the energies and plaquette expectation value between the two operator bases and find they are comparable. Additionally, we provide an explicit circuit construction for the Suzuki-Trotter implementation of the theory using the Walsh function formalism. The gate count scaling is studied as a function of the lattice volume, for both exact circuits and approximate circuits where rotation gates with small arguments have been dropped. We study the errors from finite Suzuki-Trotter time-step, circuit approximation, and quantum noise in a calculation of an explicit observable using IBMQ superconducting qubit hardware. We find the gate count scaling for the approximate circuits can be further reduced by up to a power of the volume without introducing larger errors.
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Submitted 18 November, 2022;
originally announced November 2022.
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Overcoming exponential scaling with system size in Trotter-Suzuki implementations of constrained Hamiltonians: 2+1 U(1) lattice gauge theories
Authors:
Dorota M. Grabowska,
Christopher Kane,
Benjamin Nachman,
Christian W. Bauer
Abstract:
For many quantum systems of interest, the classical computational cost of simulating their time evolution scales exponentially in the system size. At the same time, quantum computers have been shown to allow for simulations of some of these systems using resources that scale polynomially with the system size. Given the potential for using quantum computers for simulations that are not feasible usi…
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For many quantum systems of interest, the classical computational cost of simulating their time evolution scales exponentially in the system size. At the same time, quantum computers have been shown to allow for simulations of some of these systems using resources that scale polynomially with the system size. Given the potential for using quantum computers for simulations that are not feasible using classical devices, it is paramount that one studies the scaling of quantum algorithms carefully. This work identifies a term in the Hamiltonian of a class of constrained systems that naively requires quantum resources that scale exponentially in the system size. An important example is a compact U(1) gauge theory on lattices with periodic boundary conditions. Imposing the magnetic Gauss' law a priori introduces a constraint into that Hamiltonian that naively results in an exponentially deep circuit. A method is then developed that reduces this scaling to polynomial in the system size, using a redefinition of the operator basis. An explicit construction of the matrices defining the change of operator basis, as well as the scaling of the associated computational cost, is given.
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Submitted 24 January, 2023; v1 submitted 5 August, 2022;
originally announced August 2022.
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Analytic expansions of two- and three-particle excited-state energies
Authors:
Dorota M. Grabowska,
Maxwell T. Hansen
Abstract:
The last years have seen significant developments in methods relating two- and three-particle finite-volume energies to scattering observables. These relations hold for both weakly and strongly interacting systems, and studying their predictions in limiting cases can provide important cross checks as well as giving useful insights into the general formulae. In these proceedings, we present analyti…
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The last years have seen significant developments in methods relating two- and three-particle finite-volume energies to scattering observables. These relations hold for both weakly and strongly interacting systems, and studying their predictions in limiting cases can provide important cross checks as well as giving useful insights into the general formulae. In these proceedings, we present analytic results for finite-volume excited states, recovered by expanding the general relations in powers of the interaction strength. We highlight elegant patterns that emerge, especially for excited three-particle energies, and discuss various applications of the results. The two-particle results summarized here are described in more detail in the full manuscript, and the three-particle results are detailed in a manuscript to appear.
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Submitted 22 December, 2021;
originally announced December 2021.
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Efficient Representation for Simulating U(1) Gauge Theories on Digital Quantum Computers at All Values of the Coupling
Authors:
Christian W. Bauer,
Dorota M. Grabowska
Abstract:
We derive a representation for a lattice U(1) gauge theory with exponential convergence in the number of states used to represent each lattice site that is applicable at all values of the coupling. At large coupling, this representation is equivalent to the Kogut-Susskind electric representation, which is known to provide a good description in this region. At small coupling, our approach adjusts t…
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We derive a representation for a lattice U(1) gauge theory with exponential convergence in the number of states used to represent each lattice site that is applicable at all values of the coupling. At large coupling, this representation is equivalent to the Kogut-Susskind electric representation, which is known to provide a good description in this region. At small coupling, our approach adjusts the maximum magnetic field that is represented in the digitization as in this regime the low-lying eigenstates become strongly peaked around zero magnetic field. Additionally, we choose a representation of the electric component of the Hamiltonian that gives minimal violation of the canonical commutation relation when acting upon low-lying eigenstates, motivated by the Nyquist-Shannon sampling theorem. For (2+1) dimensions with 4 lattice sites the expectation value of the plaquette operator can be calculated with only 7 states per lattice site with per-mille level accuracy for all values of the coupling constant.
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Submitted 15 November, 2021;
originally announced November 2021.
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Style-based quantum generative adversarial networks for Monte Carlo events
Authors:
Carlos Bravo-Prieto,
Julien Baglio,
Marco Cè,
Anthony Francis,
Dorota M. Grabowska,
Stefano Carrazza
Abstract:
We propose and assess an alternative quantum generator architecture in the context of generative adversarial learning for Monte Carlo event generation, used to simulate particle physics processes at the Large Hadron Collider (LHC). We validate this methodology by implementing the quantum network on artificial data generated from known underlying distributions. The network is then applied to Monte…
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We propose and assess an alternative quantum generator architecture in the context of generative adversarial learning for Monte Carlo event generation, used to simulate particle physics processes at the Large Hadron Collider (LHC). We validate this methodology by implementing the quantum network on artificial data generated from known underlying distributions. The network is then applied to Monte Carlo-generated datasets of specific LHC scattering processes. The new quantum generator architecture leads to a generalization of the state-of-the-art implementations, achieving smaller Kullback-Leibler divergences even with shallow-depth networks. Moreover, the quantum generator successfully learns the underlying distribution functions even if trained with small training sample sets; this is particularly interesting for data augmentation applications. We deploy this novel methodology on two different quantum hardware architectures, trapped-ion and superconducting technologies, to test its hardware-independent viability.
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Submitted 6 August, 2022; v1 submitted 13 October, 2021;
originally announced October 2021.
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Analytic expansions of multi-hadron finite-volume energies: I. Two-particle states
Authors:
Dorota M. Grabowska,
Maxwell T. Hansen
Abstract:
We derive analytic expansions for the finite-volume energies of weakly-interacting two-particle systems, using the general relations between scattering amplitudes and energies derived by Lüscher and others. The relations hold for ground and excited states with both zero and non-zero total momentum in the finite-volume frame. A number of instructive aspects arise in the derivation, including the ro…
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We derive analytic expansions for the finite-volume energies of weakly-interacting two-particle systems, using the general relations between scattering amplitudes and energies derived by Lüscher and others. The relations hold for ground and excited states with both zero and non-zero total momentum in the finite-volume frame. A number of instructive aspects arise in the derivation, including the role of accidental degeneracies and the importance of defining a power-counting scheme in the expansions. The results give intuition concerning the imprint of weakly-interacting systems on the energy spectrum, while also providing a useful basis for the analogous results concerning three-particle excited states, to appear.
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Submitted 13 October, 2021;
originally announced October 2021.
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Direct Detection of Bound States of Asymmetric Dark Matter
Authors:
Ahmet Coskuner,
Dorota M. Grabowska,
Simon Knapen,
Kathryn M. Zurek
Abstract:
We study the reach of direct detection experiments for large bound states (containing $10^4$ or more dark nucleons) of Asymmetric Dark Matter. We consider ordinary nuclear recoils, excitation of collective modes (phonons), and electronic excitations, paying careful attention to the impact of the energy threshold of the experiment. Large exposure experiments with keV energy thresholds provide the b…
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We study the reach of direct detection experiments for large bound states (containing $10^4$ or more dark nucleons) of Asymmetric Dark Matter. We consider ordinary nuclear recoils, excitation of collective modes (phonons), and electronic excitations, paying careful attention to the impact of the energy threshold of the experiment. Large exposure experiments with keV energy thresholds provide the best (future) limits when the Dark Matter is small enough to be treated as a point particle, but rapidly lose sensitivity for more extended dark bound states, or when the mediator is light. In those cases, low threshold, low exposure experiments (such as with a superfluid helium, polar material or superconducting target) are often more sensitive due to coherent enhancement over the dark nucleons. We also discuss indirect constraints on composite Asymmetric Dark Matter arising from self-interaction, formation history and the properties of the composite states themselves.
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Submitted 18 December, 2018;
originally announced December 2018.
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Detecting Dark Blobs
Authors:
Dorota M Grabowska,
Tom Melia,
Surjeet Rajendran
Abstract:
Current dark matter detection strategies are based on the assumption that the dark matter is a gas of non-interacting particles with a reasonably large number density. This picture is dramatically altered if there are significant self interactions within the dark sector, potentially resulting in the coalescence of dark matter particles into large composite blobs. The low number density of these bl…
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Current dark matter detection strategies are based on the assumption that the dark matter is a gas of non-interacting particles with a reasonably large number density. This picture is dramatically altered if there are significant self interactions within the dark sector, potentially resulting in the coalescence of dark matter particles into large composite blobs. The low number density of these blobs necessitates new detector strategies. We study cosmological, astrophysical and direct detection bounds on this scenario and identify experimentally accessible parameter space. The enhanced interaction between large composite states and the standard model allows searches for such composite blobs using existing experimental techniques. This includes the detection of scintillation in MACRO, XENON and LUX, heat in calorimeters such as CDMS, acceleration and strain in gravitational wave detectors such as LIGO and AGIS, and spin precession in CASPEr. These searches leverage the fact that the transit of the dark matter occurs at a speed ~220 km/s, well separated from relativistic and terrestrial sources of noise. They can be searched for either through modifications to the data analysis protocol or relatively straightforward adjustments to the operating conditions of these experiments.
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Submitted 10 July, 2018;
originally announced July 2018.
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A Chiral Solution to the Ginsparg-Wilson Equation
Authors:
Dorota M. Grabowska,
David B. Kaplan
Abstract:
We present a chiral solution of the Ginsparg-Wilson equation. This work is motivated by our recent proposal for nonperturbatively regulating chiral gauge theories, where five-dimensional domain wall fermions couple to a four-dimensional gauge field that is extended into the extra dimension as the solution to a gradient flow equation. Mirror fermions at the far surface decouple from the gauge field…
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We present a chiral solution of the Ginsparg-Wilson equation. This work is motivated by our recent proposal for nonperturbatively regulating chiral gauge theories, where five-dimensional domain wall fermions couple to a four-dimensional gauge field that is extended into the extra dimension as the solution to a gradient flow equation. Mirror fermions at the far surface decouple from the gauge field as if they have form factors that become infinitely soft as the distance between the two surfaces is increased. In the limit of an infinite extra dimension we derive an effective four-dimensional chiral overlap operator which is shown to obey the Ginsparg-Wilson equation, and which correctly reproduces a number of properties expected of chiral gauge theories in the continuum.
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Submitted 26 October, 2016; v1 submitted 7 October, 2016;
originally announced October 2016.
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Nonperturbative Regulator for Chiral Gauge Theories?
Authors:
Dorota M. Grabowska,
David B. Kaplan
Abstract:
We propose a nonperturbative gauge invariant regulator for d-dimensional chiral gauge theories on the lattice. The method involves simulating domain wall fermions in d + 1 dimensions with quantum gauge fields that reside on one d-dimensional surface and are extended into the bulk via gradient flow. The result is a theory of gauged fermions plus mirror fermions, where the mirror fermions couple to…
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We propose a nonperturbative gauge invariant regulator for d-dimensional chiral gauge theories on the lattice. The method involves simulating domain wall fermions in d + 1 dimensions with quantum gauge fields that reside on one d-dimensional surface and are extended into the bulk via gradient flow. The result is a theory of gauged fermions plus mirror fermions, where the mirror fermions couple to the gauge fields via a form factor that becomes exponentially soft with the separation between domain walls. The resultant theory has a local d-dimensional interpretation only if the chiral fermion representation is anomaly free. A physical realization of this construction would imply the existence of mirror fermions in the standard model that are invisible except for interactions induced by vacuum topology, and which could gravitate differently than conventional matter.
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Submitted 22 June, 2016; v1 submitted 11 November, 2015;
originally announced November 2015.
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Little Flavor and U(2) Family Symmetry
Authors:
Dorota M. Grabowska,
David B. Kaplan
Abstract:
We examine an effective field theory inspired by Little Flavor that demonstrates a new paradigm for generating quark and lepton masses in which the scale of new flavor physics can be at the few TeV level, and new $Z'$ and $W'$ bosons are predicted. The model possesses an approximate $U(2)^2$ vector symmetry, not the full approximate $U(2)^5$ chiral symmetry of the Standard Model or Minimal Flavor…
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We examine an effective field theory inspired by Little Flavor that demonstrates a new paradigm for generating quark and lepton masses in which the scale of new flavor physics can be at the few TeV level, and new $Z'$ and $W'$ bosons are predicted. The model possesses an approximate $U(2)^2$ vector symmetry, not the full approximate $U(2)^5$ chiral symmetry of the Standard Model or Minimal Flavor Violation models, yet flavor changing neutral currents are sufficiently suppressed. Additionally, lepton flavor violating processes, such as $μ\to 3e$, lie naturally just below experimental bounds and the down quark mass can be radiatively generated.
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Submitted 28 September, 2015; v1 submitted 18 September, 2015;
originally announced September 2015.